曲线的曲率

This paper first summarizes recent researches on this topic, and then proposes some methods for curve modeling with cubic algebraic curve based on pure geometric constraints that involve control points, tangent directions and curvatures.

然后提出了一种基于几何约束的三次代数曲线的插值方法，该方法完全通过几何量如控制顶点、切线和曲率来控制三次代数曲线的形状，使得对三次代数曲线的编辑与对三次 B-样条曲线的编辑一样灵活方便。

Finally, image morphing reality degree is defined for the first time in the research field of image morphing by computing the area between the curve and one coordinate axis, curvatures of the curve at different points, and so on.

它通过计算曲线与坐标轴，曲线插值点处的曲率和其他一些衡量标准得到。

In the first part of the paper, we construct a family of 1 parameter cubic algebraic curves interpolating four given points and two tangent lines at the endpoints, and one can manipulate the shape of cubic algebraic curves by controlling the points or the tangent line directly.

该文提出的代数曲线的结构有两种，一种是插值平面上四点及两端点切线的三次代数曲线；另一种是插值两端点、两切线及两曲率的三次代数曲线。

Properties of Curves, Surface in Three Dimensions, The First Fundamental Form

课程内容：平面与空间中曲线，曲率和挠率，全曲率，同周边不等式，曲面的基本式，平

Geodesic curvature of the pitch curve on spherical surface was introduced as a medium,through which the pitch curve on spherical surface can be changed into equivalent planar pitch curve by numerical computation method.

以曲面上曲线的短程曲率为媒介，导出了球面节曲线伸展成平面当量节曲线的算法。

One is based on the B-spline fitting to the contours;the other computes the curvature directly taking advantage of the relation of curvature and osculating circle.

一是基于轮廓的B样条拟合，通过计算拟合B样条曲线在各采样点处的曲率估算轮廓点的曲率

The shape of curve could be modified to satisfy the demand simply through the amendment of the first end curvature or the directional angle of the first port tangent vector or the weight factor of a certain curve.

该方法可以通过简单地调整某段曲线的首端曲率或该段曲线的首端切矢量的方向角或该段曲线的权因子对曲线进行调节。

In order to reduce the cost of matching, we used multiple scale technique. 4. We presented a novel method of searching for similar fragments of 3D curves. with this method, a hash vector is associated with each fixed-length fragments of 3D sherd. Each vector consists of low frequence component of Fourier-Like spectrum for the distance between profile curve and the centroid.

依据样条曲线的基本理论，研究了基于B样条的轮廓曲线的匹配方法，给出了由轮廓曲线不变量曲率和挠率构造的相似不变量的选取以及基于相似矩阵的匹配算法，并对该算法的时间复杂度作了估计，同时，将多尺度技术引入到物体轮廓的匹配问题中。

After that the contour is produced by curve fitting and the curvature of every point of the contour is calculated.

然后，用曲线拟合轮廓线，并计算曲线上各点的曲率。

By the translational and rotational velocity information, we can get the curvatures of the curve.

然后对B-spline曲线微分得到曲线上的速度和角速度资讯，根据此速度和角速度我们便可得到曲线上的曲率时间函数。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。